1) Express sin 186 ° as a function of a
positive acute angle.
9) What is the period of the graph below?
𝜋
2) If 𝑓(𝑥) = 2 cos2 𝑥, find 𝑓(( ).
(1)
6
(2)
3) Find the radius of a circle on which a
central angle measuring 40° intercepts an
arc on the circle with a length of 18 miles.
(Round answer to the nearest tenth.)
4) If cot 𝜃 < 0 and cos 𝜃 > 0, what quadrant
does 𝜃 lie in?
10) What is the period of the graph of the
equation y = -6 sin 2x?
(2) 2𝜋
(3) 𝜋
5) For all values of A for which the expression
(1)
(2)
cot 𝐴
csc 𝐴
1
1
(a) sec 𝜃
6) Which expression is equivalent to sec 60°?
(1)
(2)
(3)
sin 60°
1
(4)
cos 60°
(𝑑) tan 𝜃
12) Which is an equation of the graph shown
below?
(1) y = sin 𝑥
1
(2) y = cos 𝑥
2
(3) y = cos 2𝑥
1
(4) y = sin 𝑥
1
csc 60°
1
tan 60°
2
7) The amplitude of the graph y = 3 cos 2x is
(1) 2
(2) 𝜋
(3) 3
(4) 4 𝜋
13) Find the exact value of
(a) cos 300
8) What is the frequency of the graph of the
equation y = -sin 2x?
(1) 2
(2)
1
2
6
(b) csc 𝜃
(c) cot 𝜃
1
−2
11) For what values are the following functions
undefined?
(4) sin 𝐴
cos 𝐴
(4)
is equivalent to
(3) cos 𝐴
sin 𝐴
4
(3) 2𝜋
(4) 4𝜋
(1) -6𝜋
is defined,
4
𝜋
𝜋
(3) 1
(4) -1
(b) tan
2𝜋
3
14) As angle 𝜃 increases from 𝜋 radians to 2𝜋
radians, the cosine of 𝜃
(1) increases, then decreases
(2) decreases, then increases
(3) decreases throughout the interval
(4) increases throughout the interval
3
18) If sin 𝜃 = − and cos 𝜃 > 0, find the value
5
of tan 𝜃.
19) Write an equation of a sinusoidal graph
with an amplitude of 5, a frequency of 3, a
vertical shift of 6, and a phase shift of 10.
20) If cot (x – 10) = tan (4x), find the value of x.
15) Which graph represents the equation
1
𝑦 = cos 𝑥?
2
(1)
(3)
21) If 𝜃 is an angle in standard position and its
terminal side passes through the point
1 √3
(− , ) on the unit circle, then a possible
2 2
value of 𝜃 is
(1) 330°
(2) 60°
(2)
(3) 150°
(4) 120°
(4)
22) Name the equation of the graph.
(a)
(b)
16) Which equation is represented by the
graph?
(c)
(1) 𝑦 = 2 sin 2𝑥
(2) 𝑦 =
1
2
1
sin 𝑥
2
(3) 𝑦 =
1
2
(d)
sin 2𝑥
1
(4) 𝑦 = 2 sin 𝑥
2
17) Determine the equation of the graph.
23) a) On the same set of axes, sketch the
1
graphs of 𝑦 = sin 𝑥 and 𝑦 = 𝑐𝑜𝑠 𝑥
2
over the domain −𝜋 ≤ 𝑥 ≤ 𝜋.
b) For how many intervals does
1
sin 𝑥 = 𝑐𝑜𝑠 𝑥 ?
2
24) a) On the same set of axes, sketch the
1
graphs of 𝑦 = sin2 𝑥 and 𝑦 = 𝑐𝑜𝑠2𝑥
2
over the domain 0 ≤ 𝑥 ≤ 2𝜋.
b) For how many intervals does
1
sin2 𝑥 = 𝑐𝑜𝑠2𝑥 ?
2